Kabul , Afghanistan -LRB- CNN -RRB- -- Seven insurgents were killed when a group of more than a dozen men launched an early morning attack on Bagram Air Base in Afghanistan on Wednesday , officials said .

Army spokesman Lt. Col. Clarence Counts said that five service members were wounded in the attack and a building suffered minor damage . He said the attack included rockets , small arms and grenades .

Taliban spokesman Zabiullah Mujahid told CNN that 20 armed men wearing suicide vests stormed the base around 4 a.m. -LRB- 7:30 p.m. Tuesday ET -RRB- , with four of them detonating explosives at the entrances to allow the other men to move in . Mujahid said that a `` major firefight '' took place inside the base .

But Army Specialist Christina Dion , a spokeswoman who both lives an works on the base , told CNN that personnel were ordered to enter bunkers when the base came under attack and were allowed to return to their huts and tents about 90 minutes later .

`` We 're always prepared to deal with attacks on our base , '' Counts said . `` The response this morning was immediate . ''

The fighting eventually tapered off about 7:30 a.m. local time , said NATO spokesman Lt. Col Todd Breasseale .

Another Bagram spokeswoman , Maj. Virginia McCabe , could not say if flights into and out of the air base had been stopped and said that authorities are investigating how the incident started .

`` Established security procedures are in place , '' she said , adding that personnel with `` mission-essential '' responsibilities were continuing to work .

Bagram is a heavily fortified base , its perimeter guarded by high fences and thick , concrete walls . Dion said she did n't believe anyone could have made their way into the main portion of the base .

Taliban fighters have lobbed rockets into the base in previous attacks .

CNN 's Adam Levine and Paula Hancocks contributed to this report .

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Five service members hurt , building damaged in attack using rockets , small arms , grenades

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Personnel ordered to bunkers for 90 minutes after airbase attacked , Army spokeswoman says

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Taliban spokesman says 20 armed men in suicide vests stormed base in `` major firefight ''